Vulnerability of Synchronization in Complex Networks due to the Existence of Chaotic Saddles

该提案的主要目标是研究网络系统中的瞬态混沌的作用。混沌鞍的存在可以通过在特定时刻扰动网络中的一个单元（同步的状态依赖脆弱性）来导致最初完全同步的网络的完全去同步化。我们将研究从全局稳定的同步状态到完全去混沌状态的转变的动力学起源，并阐明是否甚至是混沌吸引子而不是鞍点取决于单元的耦合强度和网络拓扑结构。此外，我们将研究这种超持续混沌行为的统计特性，例如违反瞬态混沌的标度律，并将其与噪声诱导的吸引子进行比较，以找到共性和差异。此外，我们将确定不同类别的系统中，状态依赖的脆弱性发生，以证明其普遍性。这些类别与混沌鞍形的形成机制有关：盆地边界变形、边界危机和周期叠加级联。最后，我们将研究在生态学以及大脑和心脏动力学的不同应用，以设计控制策略，以保持同步状态稳定或打破同步。

The main objective of this proposal is to study the role of transient chaos in networked systems. The presence of chaotic saddles can lead to complete desynchronization of initially completely synchronized networks by perturbing one unit in the network at a particular time-instant (state-dependent vulnerability of synchronization). We will investigate the dynamical origin of the transition from the globally stable synchronized state to the completely desynchronized state, and clarify whether even a chaotic attractor instead of a saddle is established depending on the coupling strength of the units and the network topology. Furthermore, we will study the statistical properties of this super-persistent chaotic behavior e.g. the violation of the scaling laws for transient chaos and compare it with noise-induced attractors to find commonalities and differences. Moreover, we will identify different classes of systems in which state-dependent vulnerability occurs to prove its generality. Those classes are related with the mechanisms in which chaotic saddles appear: basin-boundary metamorphosis, boundary crisis and period-adding cascades. Finally, we will study different applications in ecology as well as in brain and heart dynamics in order to design control strategies either to keep the synchronized state stable or to break synchrony.